Structure-Property Correlation in Sodium Borophosphate Glasses Modified with Niobium Oxide

Abstract

Bulk glasses of the series (100−x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ with x = 0–48 mol% B₂O₃ were prepared by slow cooling in air. Their glass transition temperature increases within the range of 0–16 mol% B₂O₃, but further additions of B₂O₃ result in its decrease. Their structure was investigated by Raman, ¹¹B, and ³¹P MAS NMR spectroscopy. The relative number of BO₄ units decreases with increasing B₂O₃ content, while the number of BO₃ units increases up to 59 % at x = 48. The upfield shift of a broad resonance peak in the ³¹P MAS NMR spectra is ascribed to an increasing connectedness of the structural network with increasing B₂O₃ content. Strong Raman band at 916–929 cm⁻¹ shows on the presence of NbO₆ octahedra in the structural network of these glasses. With the B₂O₃ addition, a decrease in DC conductivity is observed, which is attributed to the decrease in the concentration of Na⁺ ions.

1. Introduction

Sodium borophosphate glasses were studied during the last years in several papers. Sodium borophosphate glasses containing phosphorus oxide and boron oxide are termed also as glasses revealing mixed glass former effect (MGFE).

A glass-forming region in the ternary system can be found, e.g., in the paper of Ducel and Videau [1], where the authors studied the compositional series, (1 − x)NaPO₃-xNa₂B₄O₇. On the Na₂O-P₂O₅ site, it starts at P₂O₅ and reaches up to 60 mol% Na₂O, while on the Na₂O-B₂O₃ site it starts at B₂O₃ and reaches only to 40 mol% Na₂O. It is interesting that in the binary system of two glass-forming oxides, their mutual combination of B₂O₃ + P₂O₅ is not glass but only the crystalline compound, BPO₄. Its structure consists of BO₄ and PO₄ tetrahedra. Sodium borophosphate glass matrices are interesting for many applications, such as hosts for rare-earth dopants for fiber amplifiers [2,3], hosts for metallic dopants in ion-conducting glasses [4,5] and sealing glass applications [6].

Zielniok et al. [7] prepared and studied glasses at the edge of the glass-forming region having the composition (Na₂O)_0.4[(B₂O₃)_x(P₂O₅)_1−x] and within the whole range of x = 0–1. Compared to binary sodium phosphate and borate glasses, the extent of network polymerization is increased namely within the region of 0–40 mol% B₂O₃ by the formation of four-coordinate borate units, BO₄. Glasses with a higher B₂O₃ content contain also three-coordinate BO₃ units which appear to interact only weakly with phosphorus [7].

Carta et al. [8] studied glasses in the system 40P₂O₅-xB₂O₃-(60 − x)Na₂O. They reported that increasing additions of B₂O₃ resulted in the improvement of thermal stability with respect to devitrification, and an increase in hygroscopicity stability. Authors [8] discussed such evolution of properties by considering a global increase in bond strength and cross-linking of the glass network by the formation of P–O–B bonds.

A compositional line of sodium borophosphate glasses (NaPO₃)_1−x-(B₂O₃)_x was studied in the paper by Raskar et al. [9] by NMR and XPS. The authors prepared glassy samples within the concentration range of 0–30 mol% B₂O₃ by cooling the melt on the copper plate. Obtained XPS data provided a quantitative distinction between B–O–B, B–O–P and P–O–P linkages as well as nonbridging oxygen atoms. Additions of B₂O₃ to NaPO₃ produce a significant increase in the glass transition temperature from 284 °C at NaPO₃ to 421 °C in the glass with 30 mol% B₂O₃. Up to 20 mol % B₂O₃, all the boron atoms are in the tetrahedral BO₄ coordination. Rincke and Eckert [10] investigated another compositional line of sodium borophosphate glasses Na₂O-BPO₄. They prepared glasses of the (Na₂O)_x-(BPO₄)_1−x compositional line, inside the ternary Na₂O-B₂O₃-P₂O₅ system, with Na₂O content of 25–55 mol%. For structural analysis, they applied XPS, Raman and ¹¹B and ³¹P NMR spectra as well as rotational-echo, double-resonance (REDOR) NMR techniques for the study of interatomic interactions. At low Na₂O content, BO₄ units dominate, but their amount decreases as the BPO₄ content decreases and simultaneously the amount of trigonal BO₃ units increases from 14% to 33% at x = 0.55. The ³¹P MAS NMR spectra show the successive depolymerization of the phosphate units with increasing alkali oxide content. Heteroatomic P–O–B linkages are preferred in these glasses over homoatomic B–O–B and P–O–P linkages and with increasing Na₂O content the concentration of P–O–B linkages decreases, accompanied by the decrease in the number of bridging oxygen. With increasing Na₂O content and thus decreasing number of bridging oxygen species, the reticulation of the network decreases, which is reflected in the decreasing glass transition temperature. The authors [10] also reported that the BO₃ units are primarily bound via B–O–B bonds to the BO₄ units.

Structural studies of the mixed glass former system of sodium borophosphate glasses with 35 mol% Na₂O were published in papers [11,12,13]. The authors [11,12,13] investigated glass series 0.35Na₂O + 0.65[xB₂O₃ + (1 − x)P₂O₅] and compositional dependence of their density, molar volume [11] and the glass transition temperature [12] with the support of data on their structure published in paper [13]. This paper contains ¹¹B and ³¹P MAS NMR spectra and also Raman spectra of the glass series 0.35Na₂O + 0.65[xB₂O₃ + (1 − x)P₂O₅]. The authors [13] exclude the formation of BPO₄ units in these glasses and confirm the important role of internetwork bonding through B–O–P linkages. The preferential formation of tetrahedral boron groups in the borophosphate glasses is explained by the reaction of BO₃ groups with metaphosphate Q² groups giving rise to BO₄ and Q³ phosphate groups.

The structural changes in the glass network induced by the replacement of one glass-forming oxide with another, usually, have positive implications on the transport of alkali ions. For instance, in the mixed glass former system 0.35Na₂O + 0.65[xB₂O₃ + (1 − x)P₂O₅], 0 ≤ x ≤ 1 [14], the ionic conductivity changes non-monotonic reaching the maximal value of σ_DC = 2.34 × 10⁻⁹ (Ωcm)⁻¹ at glass composition x = 0.4. Since the concentration of sodium ions is kept constant throughout the entire series, the observed conductivity changes are directly related to the variations in the structural units and their influence on the mobility of sodium ions.

Further, Raguenet et al. [15] studied glasses of composition 45Li₂O-55[xB₂O₃–(1 − x)P₂O₅], 0 ≤ x ≤ 1 and reported that the non-monotonic change in the ionic conductivity correlates well with the number of BO₄ units in the glass network. In particular, at the highest concentration of boron oxide, the ionic conductivity decreases due to the formation of BO₃ units which break the conduction pathways formed by BO₄ structural units which have a favorable effect on the dynamics of lithium ions. A similar positive correlation between ionic transport and formation of mixed structural units was also reported for the system where third glass forming oxide is added (100 − x)[0.5Li₂O-0.1B₂O₃-0.4P₂O₅]-xGeO₂, x = 0–25 mol% [16].

In our previous study [17], we observed that the chemical durability of the alkali borophosphate glasses increases significantly with the addition of niobium oxide. Therefore, in the present study of sodium borophosphate glasses to improve the chemical durability of the starting sodium phosphate glass, we applied a 20 mol% addition of niobium oxide and thus we started our glass series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃, with the composition of 40Na₂O-20Nb₂O₅-40P₂O₅. We have determined the basic physicochemical properties of these glasses and for the structural investigation, we used Raman spectroscopy and ¹¹B and ³¹P MAS NMR spectroscopy. In addition, the influence of glass composition and structure on electrical conductivity over a wide range of temperatures and frequencies has been studied.

2. Materials and Methods

Glasses of the Na₂O-Nb₂O₅-P₂O₅-B₂O₃ system were prepared by melting Na₂CO₃ (99%; Sigma-Aldrich, Saint Louis, MO, USA), Nb₂O₅ (99.9%; Sigma-Aldrich, Saint Louis, MO, USA), H₃PO₄ (85 wt%, p.a.; Penta) and H₃BO₃ (99.5%; Sigma-Aldrich, Saint Louis, MO, USA) using a total batch weight of 20 g. The homogenized starting mixtures were slowly calcined up to 600 °C with the final calcination at a maximum temperature for 2 h in order to remove the water. The reaction mixtures were then melted at 1100–1250 °C under ambient air in a platinum crucible. The melt was subsequently poured into a preheated graphite mould (T < T_g) and the obtained glasses were then cooled to room temperature. The weight of the glass sample, together with the remaining glass in the crucible, was usually more than 98.5 wt% and thus the weight loss was usually less than 1.5 wt%. We, therefore, considered the batch compositions as reflecting the actual compositions. The amorphous character of the prepared glasses was checked by X-ray diffraction analysis (not shown).

The glass density, ρ, was determined using a helium gas pycnometer AccuPyc II 1340, where the volume of the sample was measured by calculating the volume of the helium gas displaced by the sample. The molar volume, V_M, was calculated using the expression ${\mathrm{V}}_{\mathrm{M}}=\overline{\mathrm{M}}/\mathsf{\rho }$, where $\overline{\mathrm{M}}$ is the average molar weight of the glass composition a∙M(Na₂O) + b∙M(Nb₂O₅) + c∙M(P₂O₅) + d∙M(B₂O₃), calculated for a + b + c + d = 1.

The thermal behaviour of glasses was studied on DTA 404 PC (Netzsch) operating in the DSC mode at a heating rate of 10 °C min⁻¹ over the temperature interval 30–1000 °C. The measurements were carried out with 100 mg powder samples, obtained by milling bulk glasses in the laboratory vibrational mill. Glass transition temperature, dilatometric softening temperature and thermal expansion coefficient were determined from the dilatometric curves using thermomechanical analyser Netzsch TMA 402. The coefficient of thermal expansion, α, was determined as a mean value in a temperature range of 150–250 °C. The glass transition temperature, T_g, was determined from a change in the slope of the elongation versus temperature plot and the dilatometric softening temperature, T_d was obtained from the maximum of the expansion trace corresponding to the onset of viscous deformation under an applied load.

The linear refractive indices at 453, 532, 637, 829 and 1062 nm were measured by the prism coupling method, using a Metricon Model 2010/Mat. Linear refractive index values, n_d (587.6 nm), were obtained from the dispersion curve calculated with Metricon software.

Electrical properties were obtained by measuring complex impedance using an impedance analyzer (Novocontrol Alpha-AN Dielectric Spectrometer) in a frequency range from 0.01 Hz to 1 MHz at temperatures from −60 °C to 240 °C. The temperature was controlled to an accuracy of ±0.2 °C. For the electrical measurements, gold electrodes, 6 mm in diameter, were sputtered onto both sides of disks using Sputter Coater SC7620.

Raman spectra in the range 1400–200 cm⁻¹ were measured on glassy bulk and crystalline powder samples at room temperature using a DXR Raman spectrometer Thermo Scientific with a 532 nm solid state (Nd: YAG) diode pumped laser.

The ³¹P MAS NMR spectra were measured using a BRUKER Avance 400 spectrometer with a 4 mm probe. The spinning speed was 12.5 kHz. The pulse length was 1.2 μs (π/4), and the recycle delay was 60 s, which was sufficient to enable relaxation at this field strength. The ¹¹B MAS NMR spectra were measured on a BRUKER Avance 800 spectrometer with a 2.5 mm probe. The spinning speed was 20 kHz. A rotor synchronized echo was used with selective pulse lengths of 20 μs and 40 μs for the first and the second pulse, with a 10 s recycling delay. The Larmor frequencies were 162.3 MHz and 128.4 MHz for ³¹P and ¹¹B, respectively. The chemical shifts of ¹¹B nuclei are given relative to BPO₄ at −3.6 ppm, those of ³¹P are relative to 85% H₃PO₄ at 0 ppm.

An EMPYREAN PANAnalytical diffractometer with Cu Kα radiation was used for the identification of crystalline phases. A database of inorganic compounds from the International Center of Diffraction Data [18] was used for the phase identification.

3. Results and Discussion

3.1. Glass Properties

Seven glasses of the compositional series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ were prepared and studied. Their composition is summarized in

Table 1. Composition, density, ρ, molar volume, V_M, glass transition temperature, T_g, dilatometric softening temperature, T_d, the coefficient of thermal expansion, α, and the index of refraction, n_d, of (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ glasses.

Na2O	P2O5	Nb2O5	B2O3	ρ ± 0.02	VM ± 0.5	Tg ± 2	Td ± 1	α ± 0.5	nd ± 0.005
Batch/mol%				g∙cm−3	cm3∙mol−1	°C		ppm/°C	[-]
40	40	20	0	3.06	44.01	496	539	16.4	1.655
36.8	36.8	18.4	8	3.05	42.5	525	559	15.3	1.658
33.6	33.6	16.8	16	3.01	41.23	528	561	14.6	1.658
30.4	30.4	15.2	24	2.96	40.22	513	555	13.4	1.656
27.2	27.2	13.6	32	2.92	39.7	510	547	12.6	1.644
24	24	12	40	2.84	38.87	484	530	12.2	1.629
20.8	20.8	10.4	48	2.73	37.88	458	534	11.8	1.618

. All glasses were homogeneous and colorless. Their basic properties (density, molar volume, glass transition temperature, the dissolution rate and the coefficient of thermal expansion) were measured and the obtained data are shown in Table 1. Figure 1 shows the densities (ρ) and molar volumes (V_M) as a function of the B₂O₃ content. Both parameters decrease in a monotonous way. The decrease in density results from the difference in the molar mass of the parent glass 40Na₂O-20Nb₂O₅-40P₂O₅ (M = 134.73) and the boron oxide B₂O₃ (M = 69.62) replacing the base glass. A decrease in the molar volume results from the replacement of the average number of atoms 5.4 in a fictive molar unit of the base glass by 5 atoms in the molecule of boron oxide with two small boron atoms.

We also measured the linear refractive index of the glasses. Compositional dependence of the obtained values of the refractive index at 587.6 nm are given in Table 1. It is evident that in the studied glass series the refractive index slightly decreases with an increasing B₂O₃ content. Nevertheless, we know that the main role in the optical properties of the studied glasses is played by the number of Nb-O bonds having large polarizability [19] and thus, the refractive index decreases with the decreasing Nb₂O₅ content.

3.2. Thermal Behavior

DTA curves of (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ glasses are shown in Figure 2. As can be seen from this figure, starting glass without B₂O₃ reveals on its DTA curve both exothermic crystallization peak followed by an endothermic peak of melting the crystalline phase. Glasses with 8 and 16 mol% B₂O₃ do not reveal any crystallization peaks on their DTA curves and thus B₂O₃ additions increase their thermal stability. On the DTA curve of glasses with higher B₂O₃ content (24–48 mol% B₂O₃), we can see one crystallization peak within the region of 700–800 °C, the intensity of which increases with increasing B₂O₃ content. It was possible to determine the values of the glass transition temperature, but more accurate data were obtained from thermomechanical measurements.

Glass transition temperature, T_g, was obtained from thermomechanical analysis and its values are given in Table 1. Compositional dependence of T_g values on the B₂O₃ content is shown also in Figure 3. Glass transition temperature increases in the studied glass series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ within the range of 0–16 mol% B₂O₃, but further additions of B₂O₃ result in a decrease of T_g from its maximum value of 528 °C at x = 16, down to the value of 455 °C at the glass with x = 48 mol% B₂O₃. We assume that the first additions of B₂O₃ form B–O–P linkages resulting in the reaching of the optimum connectivity of the glass network. Further additions of B₂O₃ result in the formation of homopolar B–O–B bonds, which can be the reason for the observed decrease in T_g values. The values of the dilatometric softening temperature, T_d, reveal similar compositional dependence with the exception of the glass with 48 mol% B₂O₃, where the difference T_d−T_g is higher. The coefficient of thermal expansion decreases significantly with increasing boron content from 16.4 ppm/°C down to 11.8 ppm/°C.

3.3. Glass Structure

Raman spectra of the glass series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ are presented in Figure 4 and assignments of the bands summarized it

Table 2. Raman bands and corresponding assignment of the (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ glasses.

Raman Shift cm−1	Assignment	Ref.
248–261	O–P–O and O–Nb–O coupled deformation mode	[21]
400–470	O–P–O and O–Nb–O coupled mode	[21,22]
600–700	P–O–Bsym stretch and P–O–Psym stretch modes	[13,23]
770–824	P–O–B stretching modes	[19,23]
771	P–O–P stretching mode	[21,23]
928–934	Nb–O bonds in NbO6 octahedra	[21,24]
1211	P–O–P (Q2) stretching vibration	[21,23]

. On the spectrum of starting glass without B₂O₃, there is a dominant vibrational band of 928 cm⁻¹. The intensity of this band decreases with increasing B₂O₃ content in the glasses, as the niobium content in the glasses decreases from 20 mol% Nb₂O₅, at the glass with x = 0, down to the 10.4 mol% Nb₂O₅, at the glass with x = 48 mol% B₂O₃. This Raman band is ascribed to the vibrations of Nb–O bonds in NbO₆ octahedra. Raman scattering on these octahedra is more effective than on the phosphate tetrahedra and therefore vibrations of phosphate units in the Raman spectra are suppressed and we can assign the vibrations of phosphate tetrahedra only the weak bands at 1211 and 771 cm⁻¹. Nevertheless, the strength of the band 928 cm⁻¹ decreases with increasing B₂O₃ content, when the Nb₂O₅ content in the glasses also decreases. In the Raman spectra of glasses with 24–48 mol% B₂O₃, we can observe an increase in the intensity of bands within the region of 773–824 cm⁻¹, which we can ascribe to the formation of complex structural units containing B–O–B units [16]. As the ¹¹B MAS NMR spectra (described hereafter) give evidence for the presence of both tetrahedral BO₄ and trigonal BO₃ units, we can await some complex borate units like tetraborate units B₄O₇²⁻, the formation of which is reported also in lithium borophosphate glasses 45Li₂O-55[xB₂O₃-(1 − x)P₂O₅] [20].

The ¹¹B MAS NMR spectra of glass series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ are shown in Figure 5a. In this figure NMR spectrum of the glass with 8 mol% B₂O₃ reveals 2 close narrow resonance signals with the chemical shift values of −1 ppm and +2 ppm in the region characteristic for BO₄ units and a small broad signal at +16 ppm in the region characteristic for BO₃ units [8]. The asymmetric shape of BO₃ resonances is due to a residual quadrupole broadening. Both BO₃ and BO₄ signals are well separated, due to the high magnetic field of 18.4T applied for the measurement, and thus it is possible to evaluate the relative number of boron atoms with tetrahedral (BO₄) and trigonal coordination (BO₃). By the decomposition of the ¹¹B MAS NMR spectra, we have obtained the compositional dependence of the amount of borate structural units in the studied glasses shown in Figure 5b. As can be seen from this figure the relative number of boron units with tetragonal coordination decreases with increasing B₂O₃ content, while the number of trigonal BO₃ units increases from 12 % at x = 8 mol% B₂O₃ up to 59 % at x = 48. With increasing B₂O₃ content, the shape of BO₄ resonances changes as the glass composition changes. We can observe a decrease in the intensity of the resonance at −1 ppm ascribed by Raguenet et al. [20] to the BO₄ resonances with four or three (OP) groups, and an increase in the intensity of the second BO₄ resonance at +2 ppm with less (OP) groups [20], but also with (ONb) and OB^III groups. This second resonance increases as the B₂O₃ content increases, whereas the intensity of the first resonance decreases. These changes associated with an increase in the B₂O₃ content in the studied glasses can be explained by the replacement of B–O–P bonds by B–O–B bonds and by a decrease in the number of B–O–Nb bonds.

The ³¹P MAS NMR spectra of the glass series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ are shown in Figure 6. In this figure, we can observe a broad complex resonance peak, the maximum of which shifts upfield from −10 ppm at the glass with x = 0 up to the value of −15.4 ppm at the glass with x = 48 mol% B₂O₃. A decreasing number of sodium cations in the glasses (Na₂O content decreases from 40 mol% down to 20.8 mol% at the glass with 48 mol% B₂O₃–see Table 1) is accompanied by a decreasing number of nonbridging oxygen atoms, the charge of which is compensated by the positive charge of Na⁺ ions. Therefore, in the glass series (100 − x)(40Na₂O-20Nb₂O₅-40P₂O₅)-xB₂O₃ with increasing B₂O₃ content the connectedness of the structural network has to increase.

From the one-dimensional ³¹P MAS NMR spectra, we are not able to differentiate P–O–B, P–O–P and P–O–Nb bonds; moreover, there will be also a high number of B–O–B bonds, especially in glasses with high B₂O₃ content. The higher connectedness of the structural network due to the decrease of the concentration of NBO is thus reflected by the observed shift of the maxima of resonance signal upfield, corresponding to the transformation of phosphate Q¹ units to Q² units. The shift reflects that there are on average fewer Na⁺ at the proximity of ³¹P nuclei since they change from NBO to BO₄ charge compensation. Moreover, the reality is, of course, more complex as phosphorus atoms in the network form not only P–O–P bonds but also P–O–B and P–O–Nb bonds.

The formation of NbO₆ units in the studied glasses is evident not only from the Raman spectra but also from crystallization experiments. We have annealed powder glasses at 640–700 °C (values chosen on the basis of DTA curves) for 4 hrs. The annealing process was held in platinum crucibles with the heating rate of 5 °C/min in air atmosphere. The results of the X-ray diffraction analyses of annealed samples are shown in Figure 7. In the case of annealed sample with 0 mol% B₂O₃, we were unable to determine the crystalline product (marked with "?" in the image). Glasses with 8 and 16 mol% B₂O₃ remained amorphous, and in the annealed glasses with 24–48 mol% B₂O₃ we found diffraction lines of monoclinic and tetragonal modifications of NbOPO₄. This compound, according to the previous structural studies [25,26], contains niobium atoms in NbO₆ octahedra. In the structure of α−NbOPO₄, these octahedra form chains with Nb–O–Nb linkages and also cross-connections with PO₄ tetrahedra and Nb–O–P linkages [17,27]. Crystallization processes usually change only medium-range order present in the glasses, but not short-range order structural motifs. Therefore, we are convinced that niobium atoms in the studied glasses form NbO₆ octahedra.

3.4. Electrical Properties

The electrical conductivity of (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ glasses was measured over a wide range of frequencies and temperatures. Figure 8a shows conductivity spectra at different temperatures for a glass containing 8 mol% of B₂O₃ as typical spectra for all the glasses studied. Overall, there are three distinct spectral features which can be observed in this figure: (a) frequency-independent conductivity corresponding to DC conductivity which is not attained for the lowest temperature (−60 °C), but becomes more pronounced as temperature increases, (b) frequency-dependent conductivity, so-called conductivity dispersion, at higher frequencies and at temperatures up to ≈120 °C, above which it disappears from the frequency window of the impedance spectroscopy measurement and (c) a decrease of conductivity at low frequencies and high temperatures, above 90 °C in Figure 8a. The latter feature is called the electrode polarization effect and it originates from the accumulation of sodium ions at the blocking gold electrode used in the electrical measurements.

The DC conductivity exhibits Arrhenius temperature dependence for all glasses and has characteristic activation energy, see Figure 8b. The activation energy for the DC conductivity, W_DC, was determined for individual glass samples from the slope of log(σ_DCT) vs. 1000/T using the equation:

$${\sigma }_{DC}T={\sigma }_0^{*}\exp \left(\frac{-W_{DC}}{k_{B}T}\right)$$

(1)

where ${\sigma }_{DC}$ is the DC conductivity, ${\sigma }_0^{*}$ is the pre-exponent, k_B is the Boltzmann constant and T is the temperature (K). The activation energy, W_DC, and DC conductivity, ${\sigma }_{DC}$, at 30 °C for all investigated glasses are shown in Figure 9 and listed in

Table 3. The number density of sodium ions, N, DC conductivity, ${\sigma }_{DC}$ , determined as a plateau value in the conductivity isotherms, activation energy, W_DC, for (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃, 0 ≤ x ≤ 48 mol%, glasses.

Sample	N a	W	σDCb
	cm3	eV	(Ωcm)−1
B0	1.08 × 1022	0.62	6.88 × 10−9
B8	1.04 × 1022	0.64	2.89 × 10−9
B16	9.77 × 1021	0.66	9.04 × 10−10
B24	9.10 × 1021	0.69	1.98 × 10−10
B32	8.28 × 1021	0.74	4.30 × 10−11
B40	7.50 × 1021	0.79	3.86 × 10−12
B48	6.61 × 1021	0.83	6.26 × 10−13

^a calculated from the glass composition and density; ^b values at 30 °C.

. With increasing B₂O₃ content, the DC conductivity continuously decreases over more than four orders of magnitude while the activation energy for DC conductivity, W_DC, follows the opposite trend with values increasing from 0.62 to 0.87 eV.

The observed continuous decrease in ionic conductivity with the addition of B₂O₃ can be mainly related to the decrease in the number density of sodium ions N_V, see Table 3, since B₂O₃ is added at the expense of all oxides Na₂O, Nb₂O₅ and P₂O₅. This is true for all glasses containing up to 40 mol% of B₂O₃ since they exhibit a perfect correlation between DC conductivity and N_V; note that for glasses containing 0 and 8 mol% of B₂O₃ N_V decreases only slightly, see Table 3, which is reflected in a less steep change of DC conductivity and activation energy for DC conductivity. However, glass containing 48 mol% of B₂O₃ exhibits a small but evident departure from the steep change if both DC conductivity and activation energy, which suggests that apart from the effect of the number density of sodium ions, the glass network influences the ion dynamic. The ¹¹B MAS NMR spectrum reveals that in this glass, unlike in other glasses from this series, the fraction of BO₃ units is higher than that of BO₄ units, the ratio being 59%:41%, which suggests that the formation of boron units with trigonal coordination has a facilitating effect on ion dynamics. This is in contrast to the results reported by Raguenet et al. [15] who showed that the dominance of BO₃ units causes a decrease in conductivity due to a decrease in the number of the easy conduction pathways provided mainly by BO₄ units. However, in their study [15] the glass system contained two glass forming oxides, P₂O₅ and B₂O₃ which is not the case here. Therefore, it is likely that the combination of a high fraction of BO₃ units, NbO₆ octahedra which were reported to have facilitating effect on the ionic transport [28], as well as a smaller number of NBO bonds which can act as traps for ions, causes an ease of the transport of sodium ions in the glass with the highest amount of B₂O₃.

In the following, we examine the features of the frequency-dependent conductivity of these glasses by applying the scaling procedure introduced by Summerfield [29,30]. The Summerfield scaling procedure is expressed as:

$$\left(\frac{{\sigma }^{’}\left(v,T\right)}{{\sigma }_{DC}\left(T\right)}\right)=f\left(\frac{v}{T{\sigma }_{DC}\left(T\right)}\right)$$

(2)

where f(x) denotes the scaling function, and other quantities have their usual meaning. The Summerfield scaling can be understood as mobility scaling. Its validity signifies that the only role of temperature is to speed up (as temperature increases) or slow down (as temperature decreases) the charge carrier dynamics without changing the conduction mechanism. For each glass in this study, the application of Summerfield scaling yields a conductivity master curve, see Figure 10a for 8 mol% B₂O₃ glass, indicating that the time-temperature superposition principle is valid and that the conduction mechanism for all glasses does not change with temperature. In the next step, we applied super-scaling in which individual conductivity master curves are plotted in the same graph, see Figure 10b. As can be seen from the figure, the individual conductivity master curves do not overlap and thus fail to produce a conductivity super-master curve. This is in line with previous studies [31,32] where similar shifts were related to the changes in the number density of mobile ions. However, upon application of an arbitrary shift along the scaled frequency axis all conductivity master-curves perfectly superimpose, see Figure 10c, revealing that the shape of the conductivity dispersion does not change with composition. Similar results were reported for many mixed glass-former systems [33,34].

Another parameter which can be extracted from the frequency-dependent conductivity is the typical length scale for diffusive motions of ions known as Sidebottom length, L, defined as [35]:

$$L^2=\frac{6k_B}{{\mathrm{N}}_{\mathrm{V}}{q}^2}\frac{{\sigma }_{DC}T}{f_0}$$

(3)

where f₀ is a characteristic frequency determined as from 2σ_DC. Figure 11 shows the dependence of the Sidebottom length on the amount of B₂O₃. Interestingly, the typical length scale for diffusive motions of ions exhibits three different regions; the initial increase up to 16 mol% of B₂O₃, a nearly constant value in the intermediate range of compositions and the second increase for a glass containing 48 mol% of B₂O₃. These trends correlate well with the trends in DC conductivity and indicate that short-range transport and macroscopic (DC) transport are interconnected and that are both controlled by the structural features of the glass network.

4. Conclusions

Homogeneous glasses can be prepared in the series (100 − x)[0.4Na₂O-0.2Nb₂O₅-0.4P₂O₅]-xB₂O₃ for x = 0–48 mol% B₂O₃. We have found that there is an optimum bonding relation in the glass network at about 8–16 mol% B₂O₃, where glass transition temperature reaches its maximum. We suppose that there is some space for reaching an optimum connectedness of the glass network for BO₄ groups prevailing in the glass structure at the low B₂O₃ content. It is a little paradoxical that a decrease of T_g, with further additions of B₂O_3, is associated with an increasing connectedness of the network because the number of nonbridging oxygen atoms decreases. Nevertheless, heteropolar bonds are usually preferred in the borophosphate glasses before the homopolar bonds. The Raman spectra indicated that NbO₆ coordination prevails in the studied glasses. This type of niobium coordination was supported also by the results of crystallization experiments. Investigation of ¹¹B MAS NMR spectra revealed the coexistence of both BO₄ and BO₃ units in these glasses. We believe that the observed increase in the relative number of BO₃ units can be the reason for the limit of glass formation in this glass series at 48 mol% B₂O₃. With the increase of B₂O₃ content through the glass series, the ionic conductivity decreases mainly due to a decrease in the concentration of Na⁺ ions. However, for the glass with the highest amount of B₂O₃ the facilitating effect of the glass network composed of BO₃ and NbO₆ units was observed in both short-range and long-range dynamics of sodium ions.